MATH 125 Quiz: MATH 125 UWashington Quiz125W10 ans

• School: UW
• Department: Mathematics
• Course: MATH 125
• Professor: All

Document Summary

Mathematical economics final, december 8, 2015: consider the di erential equation y 2 y + y = 0. Then nd the solution that obeys y(0) = 1, y(0) = 2. Answer: the characteristic equation is 2 2 + 1 = 0. Since = 1 is repeated, the general solution is y(t) = et + tet. Y(0) = 2 is y(t) = et + tet: minimize the function u(x, y) = x2 + y2 subject to the constraints x + y2 = 3. Answer: the hessian of u is h = (cid:18) 2. It follows that any solution to the rst-order conditions will be a local minimum. The lagrangian is l = x2 + y2 (x + y2 3). The rst-order conditions are 2x = and 2y = 2 y. If y = 0, the constraint yields x = 3. In that case = 6 and u(3, 0) = 9. If y 6= 0, = 1 which implies x = 1/2.